 
Summary: A Meshless Method for the Numerical Solution of the 2 and 3D Semiconductor
Poisson Equation
C.J. Wordelman, N.R. Aluru, U. Ravaioli1
Abstract: This paper describes the application of the mesh
less Finite Point (FP) method to the solution of the nonlin
ear semiconductor Poisson equation. The FP method is a
true meshless method which uses a weighted leastsquares fit
and point collocation. The nonlinearity of the semiconduc
tor Poisson equation is treated by NewtonRaphson iteration,
and sparse matrices are employed to store the shape function
and coefficient matrices. Using examples in two and three
dimensions (2 and 3D) for a prototypical nchannel MOS
FET, the FP method demonstrates promise both as a means of
mesh enhancement and for treating problems where arbitrary
point placement is advantageous, such as for the simulation of
carrier wave packet and dopant cloud effects in the ensemble
Monte Carlo method. The validity of the solutions and the ca
pability of the method to treat arbitrary boundary conditions is
shown by comparison with finite difference results.
keyword: finite point methods, meshless methods, mesh
